geometry
posted by Piggy on .
A regular hexagon has an area of 96sqrt3. What is the length of each side of the hexagon?

The area of a polygon of n sides with an apothem of a and side c is
A=nac/2
For a hexagon,
n=6, apothem=c*sqrt(3)/2
so
Area=6*c*(sqrt(3)/2)*c/2
=3c²sqrt(3)
In the given case,
96sqrt(3) = 3c²sqrt(3)
Solve for c (length of side).